Gas measurement and analysis system

ABSTRACT

A gas measurement and analysis system having a gas chromatograph which converts a gas mixture from a source to a time varying continuous signal. This signal is sampled and converted to digital form by an analog to digital converter which provides a stream of amplitude dependent digital values at equally spaced time intervals. These sampled signals are applied to a rate of change estimator system which provides an accurate estimate of the time derivative of the sampled signal by means of recursive digital feedback. The output of the estimator system is applied to a processor.

BACKGROUND OF THE INVENTION

A. Field of the Invention

This invention relates to the field of art of gas measurement andanalysis systems and particularly with respect to gas chromatographsystems.

B. Prior Art

Prior system have been used to achieve an estimation of the rate ofchange of a noise-burdened signal particularly in the field ofinstrumentation electronics and radar signal processing. Such signalsare characterized by having amplitudes which are of the same order asthe noise. Many forms of differentiator networks associated withoperational amplifiers exist each of which suffers in varying degreesfrom problems of extreme sensitivity, "hang-up" in the saturation modeand other undesirable nonlinear modes of operation in the presence ofnoise. Other prior systems have used filtering networks. However,filters have been limited because of size and weight. In addition,filters have provided undesirable varying amounts of amplitude and phasedistortion of the original signal when the frequency content of thesignal being processed is in the approximate spectral range of the noisebeing eliminated.

Additional prior art exists in the area of "off-line" processingtechniques in which data points are collected which contain theprocessed signal imbedded in a noise component. Digital processingmethods are used to separate the signal from the noise component byemploying analytical methods such as the "least squares" technique. Bymeans of such techniques, the primary trend of the desired function canbe determined. However, such methods are normally limited by theexcessive degree of computation time required and the necessity ofoperating in non-real time. Many operational systems require real timecomputational capability due to memory size limitations and limitedprocessing power (in terms of time) of miniprocessor and microprocessorsystems.

SUMMARY OF THE INVENTION

A system for measuring and analyzing a gas mixture which comprises a gasprocessor for producing a time varying signal which is related to theconstituents of the gas mixture. A converter samples the time varyingsignal and converts it to digital form for providing a sampled datasignal. A rate of change estimator provides a rate of change signal. Theestimator includes recursive digital feedback means coupled to an outputof the estimator and also to the converter. In this manner, there isproduced past time value signals of the estimated rate of change signaland of the sampled data signal. The estimator further comprises meansfor combining the past time value signals with the sampled data signalfor producing the estimated rate of change signal.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a gas chromatograph measurement andanalysis system including a rate of change estimator system inaccordance with the invention;

FIG. 2 is a block diagram of the rate of change estimator system of FIG.1;

FIGS. 3A-E are waveforms helpful in describing the operation of FIG. 1;

FIGS. 4A-B are waveforms of converter output and rate of changeestimator system output helpful in explaining operation of FIGS. 1 and2; and

FIGS. 5A-B are amplified segments of the output of the gas chromatographhelpful in explaining the theory of operation with and without noise.

DETAILED DESCRIPTION

Referring to FIG. 1, there is shown a gas measurement and analysissystem 10 which includes a gas chromatograph (GC). Chromatograph 15converts a gas mixture from a source applied by way of input line 12undergoing analysis to a time varying, continuous signal 14 (shown inFIGS. 3A, C) at GC detector output 14a. Signal 14 is sampled andconverted to digital form by analog/digital converter 18 to provide astream of amplitude dependent digital values (samples) 17 on line 16(FIG. 3B) to a rate of change estimator system 20 and to processor 30.System 20 provides an accurate estimate at output 21a of the timederivative 21a of signal 14.

Using signal 21 and A/D output signal 17, processor 30 computes anaccurate compositional analysis of the gas stream on line 12 currentlyunder analysis. System 10 samples the gas stream, develops a GC outputsignal 14 and computes from the intelligence of this signal thecomposition of up to 15 gas constituents or components includingnoncombustibles, saturated and non-saturated hydrocarbons.

The computed output data 36 is applied to a printer 35 by way of theinput-output controller (IOC) 24. The output data comprises thefollowing representative list of parameters: analyzer identification,time and date of analysis, gross saturated BTU/CF, real specificgravity, Z factor, total area of GC output function peaks, names of eachof the gas mixture components (methane, carbon dioxide, etc.) with eachrespective concentration to two decimal places (XX·XX%), peak retentiontimes, response factors and other important analysis information.

Status control panel 22 is used during initial system start-up andduring system repair procedures and comprises a switch light array 22and a high speed paper tape reader 34. Application and diagnosticprograms are applied to system 10 by way of a high speed paper tapereader 34. The switch light array 22 forms a control and status displayto enable the operator to command and monitor the status of the systemperformance. Keyboard 38 provides an alphanumeric input capability foruse by an operator for changing system constants, editing tabulatedvalues, entering time-date data and performing other routine diagnosticfunctions. Console 38 also displays the data currently being sent to theprinter 35 from processor 30.

I/O controller 24 comprises a plurality of programmable hardware whichformats data 41 being transferred to and from the processor 30 with twoanalog outputs for remote transmission carrying BTU and specific gravityintelligence. An output line 24a and 41 of controller 24 is effective todrive and control the converter 18 to determine its operational samplingrate r_(o). The sampling rate is varied as a function of the gas mixtureundergoing analysis. Contained in the signal on line 24a are command andstatus words associated with an auto-ranging amplifier which permitsproper processing of the broad dynamic range (5 micro-volts to 10 voltspeak) of GC detector output 14a. Controller 24 also provides signals onlines 23a, 24b which drive the status panel indicator devices 22a and tooperate the GC solenoids in GC 15 at the proper time and sequence.Controller 24 senses the state of the status control panel switches 22aand customer-provided contact closures 40. This switch data on lines 23aand 40a is communicated to the processor main operating program via aninput port polling routine.

A stored application program resides in processor 30 after being readfrom paper tape 19 via a high speed paper tape reader 34. Processor 30,upon receiving the execute command from status control panel 22sequentially executes the program instructions. The program directs theoperation of the entire system by taking data from the sourcesinterfacing the controller 24, issuing commands via the controller tothe gas chromatograph 15, transferring data to the proper output devicesuch as printer 35 and status panel indicators. A dialog is maintainingwith the operator at keyboard console 38 is required. The machine codefor a typical gas mixture program is enclosed as pages 1-21 for use onprocessor 30. This code is given in octal format with every eighthaddress location given by the left hand column in octal format.

The purpose of the rate of change estimator 20 is to determine the rateof change (derivative) with respect to time of a sampled data signal 17shown in FIG. 3B which is the digitized output of converter 18.Estimator 20 uses a minimum amount of computational components achievedby using a recursive digital feedback technique. In so doing, past timevalues of the estimated rate of change function are used to form thecurrent estimated value of the same function.

Signal 14 is representative time-wise of the constituents of the unknowngas mixture on line 12. Signal 14 is a continuous, time-varying signalwhich is sampled at equally spaced time intervals (Δt) using A/Dconverter 18, FIG. 3C. The function of the A/D converter is to sampleand digitize signal 14 and to present a stream of digital values toinput of the rate of change estimator logic. The inverse of the samplinginterval is the sampling rate or r_(o) =1/Δt. The sampling rate r_(o) isdetermined by the characteristics of the gas chromatograph analysis tobe run.

The rate of change function and the original signal are both deliveredto processor 30 to undergo feature detection provided by subroutine inthe program. The logic of this routine analyzes the GC detector outputsignal 14 and its associated derivative for the purpose of determinationof the area underneath the peaks of the GC output curve as shown in FIG.3C. Decisions on the following questions are made:

(1) Is the GC signal still at base line level?

(2) Has a chemical component begun to emerge?

(3) Has a maxima been reached?

(4) Has a decline begun?

(5) Has the declining component reached a base line?

The answers to these questions determine the logic path taken and areused to control the computation of the area A_(i) under the GC detectorsignal curve, FIG. 4A. The area under the curve y_(i) begins at thefirst departure from base line and should end at the return to baseline. This process is carried out continually in real time during thechemical analysis so that each of the emerging components is, in turn,recognized and integrated.

At the end of this analysis process, a list or table is available whichcontains the areas associated with each of the components. Next, each ofthese areas are corrected for any existing base line offset by applyinga geometric algorithm. This algorithm assumes that the base line varieslinearly with time. Given knowledge of the slope and a constant, theprogram then applies a trapezoidal correction. It is these correctedareas which are then used to compute the actual composition of thecomposite gas undergoing analysis.

The composition of the gas stream being tested is computed by applying"response factors" or "calibration factors." In principle, thepercentage or relative amount of each component in the sample isproportional to the measured area under the GC detector output curve. Inpractice, some deviations from the theoretical percentage values arefound and these are accounted for through the usage of these"calibration factors." Ideally, the calibration factors would be unity.The constituent areas are each multiplied by their respectivecalibration factor to arrive at the correct composition mix of the gasunder analysis.

Next, the processing system utilizes the computed values of thepercentages of the gas constituents to calculate the thermal heatingvalue of the gas mixture. This can be done using a tabulated list storedin memory of the heating value contribution factors for each of thecomponents. To perform this calculation, one must know the actualidentity (chemical name) of each of the detected components. Thisidentification process is performed by knowledge of the time ofemergence for each gas constituent within the GC. Through experience areliable history of emergence times has been accumulated and tabulatedin the form of a look-up table stored in memory. Therefore, the storedprogram performs a matching process of the currently observed emergencetimes against the tabulated times. Knowledge of the chemical identitypermits referencing of standard BTU contribution information for eachconstituent comprising the mixture. A computation of the weightedaverage is performed to arrive at the overall heating value of themixture.

Similar computations are performed to arrive at the specific gravity ordensity of the mixture using the specific gravity contributions of eachof the constituent components. Straightforward correction formulas areapplied to arrive at the resulting BTU value and specific gravity. Thesecorrections and adjustment techniques are published in American GasAssociation Report AGA #3. The resulting BTU value, specific gravityvalue, and the list of percentages of each of the identified componentsof the gas mixture are considered the final output of the system whichare then printed or displayed appropriately.

Effect of Noise on Rate of Change Estimator Performance

Most electronic systems suffer performance degradation in the presenceof noise. Noise refers to any spurious disturbances that tend to obscurethe signal being processed. Gas chromatograph systems are adverselyaffected by noise voltages since the amplitude of the GC detector output14a can, in some analyses, be of the same order of magnitude as averagesystem noise levels. However, the processing system must be able todistinguish between valid peaks and rapid changes in the GC detectoroutput signal and random noise spikes in addition to other unwanted longterm disturbance associated with base line drift.

Noise impulses have an inherently broad frequency content. Rate ofchange detection and computational logics similarly have responsefunctions which are of the form of the following equation and thereforeare highly sensitive to noise impulses.

    E.sub.out =jω·E.sub.input where ω=2πf (1)

In the case of operational amplifier differentiator devices, noiseimpulses cause rapid amplifier saturation states and subsequent longterm "hang-up" conditions.

Examining the amplitude function of GC detector output signal 14, FIGS.3C, 4A, the task of system 10 is to determine the area A_(i) bounded bythe function y_(i) and an arbitrary base line. The base line is thecentral value of the residual system noise when the system is notactively processing a sample. This area is determined by knowledge ofwhen the function commences its rise (t_(i).sbsb.1), peaks(t_(i).sbsb.2) and terminates its decline (t_(i).sbsb.3), FIG. 4A. Onemethod of performing this area determination involves accurate knowledgeof the behavior of the derivative function dy(t)/dt. Hence, the needarises for a rate of change estimator circuit to determine this timederivative function in real time.

A performance trade-off exists in the design of a system which mustrespond to rapid signal variations in the presence of noise and yetavoid unwanted system response (as subsequent decisions) to rapid ratesof change associated with noise impulses. The rate of change estimatorlogic must be sufficiently sensitive to detect small rates of signalchange associated with gas components which propagate through the GCtubing in a longer time distributed manner. It is the time derivativefunction that permits detection of the emergence of various gascomponents traveling through the chromatograph 15. The chromatograph isessentially an instrument that has a baseline output which is punctuatedby deviations from the baseline as shown in FIG. 3C. These deviationstend to be bell-shaped curves somewhat like the statistical normal curveof error. Measurement of the areas under the GC output function of tenpeaks, for example, will indicate the proportional amounts of 10constituents of the gas sample injected into the GC. Therefore,different gas components arrive at the GC detector at different times.System 10 is effective to individually compute the area under each ofthese bell-shaped deviations. Performing this computation isstraightforward in principle. In practice, difficulties arise whencalculating a derivative from real information because the effects ofnoise are amplified in the calculation. The derivative forming processis more sensitive to noise than to the original signal because of thehigher rates of voltage change associated with noise pulses.

system 20 provides an effective solution to these problems caused bynoise by employing a recursive technique. Recursive implies that thesignal output (digital word) of a previous computation time is used asan input data word during the current computation time. The use ofmemory is therefore required to permit the computational logic toprocess prior (historical) values of the signal.

System 20--Theory of Operation

The function of the rate of change estimator system 20 is to determinethe average rate of change of a noise-burdened signal y(t) as shown inFIG. 5B. It may be assumed that the time elapsed between adjacentsamples is Δt and is constant for a specific application. Applying thesimplest form of calculation to the waveform shown in FIG. 5A, we wouldtake differences between successive values of y(t) and call that anestimate of the derivative. Thus, in symbolic form: ##EQU1## The problemwith this approach is its extreme susceptibility to noise as the sampletime decreases. Extreme care is required in later processing if anyuseful results are to be achieved.

It can be seen that these values of the derivative would vary radicallyfrom one sample time to the next if noise impulses are considered:##EQU2## where δ_(Ni) represents the instantaneous noise voltage to beinstantaneously superimposed upon the GC detector output signal of FIG.5A.

The process herein for forming the derivative employs signal amplitudeaveraging over a large time interval (larger quantity of samples)thereby cancelling short term noise deviations. Referring again to FIGS.5A and 5B, y(t) depicts a small segment of a GC peak waveform or curveand is shown to be noise free, smooth and continuous. Let k represent anextended number of sample times. If k=16, the rate of change estimator20 will be programmed to use a 16 point computational sequence. To formthe estimated derivative, we take the signal amplitude (y_(o)) at thebeginning of a 16 sample intervals and subtract it from the next 15successive amplitude values of y(t), and then sum these differences.##EQU3## Note that Δy/Δt (avg) is proportional to the average rate ofchange of y(t) during the period defined by kΔt seconds. Thus, we areperforming a differentiation process by doing an integration orsummation process.

Examining FIG. 5B, it can be seen that when the noise function δ_(N) (t)is superimposed upon y(t), it will be additive to some of the samplesand subtractive from others. It is found that the noise voltage will becancelled out over a sufficiently long time interval. Thus, by addingthe computed differences over an extended time period, an advantage ofcancelling out the noise function δ_(N) (t) occurs. However, theobjective of determining the average rate of change has been met.

System 20 uses a recursive technique which is substantially equivalentto the process defined by equation 4. Certain precautions must beobserved to avoid possible round-off error in the logic circuit. Bothtechniques (equation 4 and 5) can be shown to provide the same numericalrate of change magnitude. The advantage of the recursive technique isthat much less circuitry is required for implementation and execution isfaster. In the prior example using 16 samples, it was required toperform 15 subtractions and additions. In a real time processing system,this plurality of operations could possibly prevent the system fromkeeping abreast with the total computational task. Hence, the recursivetechnique disclosed is much more efficient than the basic definition ofthe process defined by equation 4.

    F.sub.i ·(Δt)=F.sub.i-l ·(Δt)+y.sub.i+k -y.sub.i -k(y.sub.i -y.sub.i-l)                           (5)

where

F_(i) =estimate of the average rate of change of the input signal

i=time indexing parameter (i=1,2,3, . . . n), (ith instant)

y=amplitude of input signal

k=sampling parameter

System 20 delays the input signal such that it can compute using severalvalues available to it simultaneously. This delay function is performedusing shift register techniques. The parameter k is used directly inequation 5 as a multiplier which permits adjustment of the behavior ofthe system 20. By increasing k, a larger sample quantity may be used andsystem 20 rejects larger amounts of high frequency noise components. Inpractice, the parameter k is adjusted for a specific GC application.

Referring now to FIG. 2, in system 20, an arbitrary binary word 17 givenby y_(i+k) represents an output data word of 32 bit length from the A/Dconverter 18, FIG. 1. This data word is one of a series of data wordsshown in FIG. 4A. Upon receiving a start command (bar indicates activelow logic levels) on line 68, the Q output 41 of RS flip-flop 71 goesactive high (RUN) and is used to command the converter 18 to commencethe conversion process. The Q output of flip-flop 71 resets the firststage of a shift register array 44 and 32 bit latch registers 44 and 60.Prior to the arrival of the end of conversion signal 42 from converter18, a stop command on line 69 is sent from controller 24 thereby placingthe Q,Q outputs 41 and 65 of flip-flop 71 in the inactive state. Uponarrival of the end of conversion status signal 42 from converter 18, thedata sample currently being sent from converter 18 is clocked into shiftregister array 44. Latch registers 44 and 60 are similarly strobed bysignal 42 to store the data words present on their respective inputlines. Shift register array 44 comprises a bank of flip-flops forming a32 times k array of 1 bit storage elements. The function of this arrayis to deliver the data sample y_(i) on line 46 which occurred k samplesago in the past, the y_(i+k) signal on line 16. Hence, array 44 is aform of digital delay device which can be programmed to achieve k Δtunits of time delay.

Shift register array 44 delivers signal y_(i) on line 46 to a digitalsubtractor device 50a. Device 50a performs a subtraction operation F=A-Bto yield the signal (y_(i+k) -y_(i)) on line 77. Each element of device50a processes a 4 bit slice of each of the two 32 bit words y_(i+k),y_(i) currently existing on the inputs A and B. A similar subtractordevice 54 forms the term y_(i) -y_(i-l) on line 55. The term y_(i-l) online 52 is formed using a 32 bit latch register whose function is toprovide a storage delay of 1 sample time, Δt.

The term (y_(i) -y_(i-l)) is now applied to the input of the kmultiplier 57 where k has been assumed to be set at a value 16. Thesignal on line 55 is strobed into the lower 32 bit positions of the 40bit shift register 57 comprised of five 8 bit shift registers.Thereafter, the data word y_(i) -y_(i-l) is shifted 4 bit places towardsthe most significant bit end of the shift register 57 therebyaccomplishing a multiplication operation of 2⁴ or 16. The series ofshift clock pulses 70 and input/output mode control signals 80 to device57 are developed by and sent from logic contained in the controller 24to yield at the appropriate time on line 56 the signal k(y_(i)-y_(i-l)). This signal is then applied to the A input of device 50bwhich performs the subtraction function F=B-A. The variable k is relatedto the quantity of samples which are necessary and sufficient toadequately remove the noise component δ(t). The parameter k is shown tobe set at 16 but in practice could be a smaller or larger integerdepending upon the severity of the noise voltage swings. Hence, the kmultiplier device 57 could take the form of a programmable arithmeticlogic unit. If k were programmable, then shift register array 44 wouldalso be comprised of additional logic gates to provide an associatedreconfiguration so as to always achieve a delay of k Δt sample times.

The signal F_(i) ·(Δt) on line 21a is applied to a 32 bit wide latchregister 60 similar to latch register 44. Device 60 is similarly clearedand clocked with the signals 65 and 42 respectively thereby providing asingle sample time delay and consequently the signal F_(i-l) (Δt) online 58. Line 58 supplies the "B" data inputs to the previouslydiscussed subtractor 50b. Device 50b is identical to devices 50a, 54,and 50c but is programmed to provide the arithmetic function F=B-A online 78. Given the input terms as shown on wires 56 and 58, device 50bdevelops an output signal F_(i-l) ·(Δt)k(y_(i) -y_(i-l)) on line 75which is applied to the B input of adder device 50c. Device 50c providesthe arithmetic function F=A+B thereby yielding at its output thefunction F_(i) ·(Δt), the estimation of the time derivative of the GCdetector output.

It will be understood that the signal F_(i-l) on line 58 represents theprior (one sample time) estimate of the time derivative and this term isutilized to form the current estimate of the rate of change. The signalon line 21a lags input function 17 on line 16 by a period of k sampletimes.

While particular embodiments of the invention have been shown anddescribed, this is not to be considered as necessarily limiting of theinvention, it being understood that numerous changes may be made withinthe scope of the invention to suit the technical requirements ofparticular applications. For example, it will be understood that system20 may be implemented in the form of a program by processor 30. Further,in an analog form of system 10, instead of an A/D converter 18, ananalog sample may be provided by a sample and hold circuit, for example,and estimator system 20 may be designed as an analog system withprocessing as desired. Still further in the analog form, signal 14 maybe taken without sampling and estimator system 20 would estimate inanalog form on a continuous basis. The analog output of system 20 maythen be sampled as desired in accordance with the processing being used.

                  TABLE OF COMPONENTS                                             ______________________________________                                        In systems 10 and 20, the following components                                provide the operation and function herein described.                          Reference                                                                     Character                                                                             Component     Type                                                    ______________________________________                                        15      gas chromatograph                                                                           EAI 85.0001 (PR-250)                                                          Electronic Associates, Inc.                             18      A/D converter EAI 22.1311 & 40.0788-1                                 22      status control panel                                                                        EAT 20.1348                                             24      I/O controller                                                                              EAI 2214 1172, 22.1228-3                                                      40.0792-7, 22.1233                                      30      processor     EAI Datapacer 46.0221                                   44      shift register                                                                              74 164 (64x)                                            48,60   register      74 273 (4x)                                             50a-c, 54                                                                             adder/subtractor                                                                            74S381 (8x)                                             57      multiplier    74S299 (5x)                                             ______________________________________                                    

What is claimed is:
 1. A system for measuring and analyzing a gasmixture comprisinggas processing means for producing a time varyingsignal related to the constituents of the gas mixture, means forsampling and converting to digital form said time varying signal therebyto provide a sampled data signal, and digital estimator means forproviding a rate of change estimate signal with respect to time of saidsampled data signal, said digital estimator means including (1)recursive digital feedback means coupled to an output of said digitalestimator means for producing at least one past time value signal of theestimated rate of change signal and (2) feed forward means coupled tothe sampling means for producing at least one other past time valuesignal of the sampled data signal, means for combining both past timevalue signals with the sampled data signal for producing a signal areadefined for an interval and above the amplitude of one of said past timevalue signals thereby providing the estimated rate of change signal. 2.The system of claim 1 in which said sampling means includes means forproviding said sampled data signal whose amplitude is a function of thegas constituents.
 3. The system of claim 1 in which said sampling meansincludes means for sampling said time varying signal at equally spacedtime intervals to provide said sampled data signal in the form of aseries of equally spaced amplitude dependent digital signals.
 4. Thesystem of claims 1, 2 or 3 in which said feed forward means includesmeans for delaying the sampled data signal from said sampling means by apredetermined number of sample times thereby to produce a delayedsampled data signal as the other past time value signal.
 5. The systemof claim 4 in which said feed forward means includes means for furtherdelaying said delayed sampled data signal, and means for producing thedifference between said delayed sampled data signal and said furtherdelayed sampled data signal and for multiplying the resultant signal bysaid predetermined number of sample times to produce a multiplieddifference signal.
 6. The system of claim 5 in which said recursivefeedback means includes further means for delaying the rate of changeestimate signal to provide a delayed rate of change estimate signaldelayed by one time interval, and further means for combining saiddelayed rate of change estimate signal and said multiplied differencesignal for producing a recursive past time value signal.
 7. The systemof claim 6 in which said combining means includes means for combiningsaid recursive past time value signal and said delayed sampled datasignal with the sampled data signal for producing said estimated rate ofchange signal.
 8. The system of claim 4 in which there is providedprocessing means for performing analysis of said rate of change estimatesignal to provide the composition of the constituents of the gasmixture.
 9. A system for gas measurement and analysis comprisinggasprocessing means for producing a time varying signal related to the gas,means for sampling said time varying signal thereby to provide a sampleddata signal, and estimator means for providing a rate of change estimatevalue with respect to time of said sampled data signal, said estimatormeans including (1) means for recursively feeding back an output of saidestimator means for producing at least one past time value of theestimated rate of change value and (2) means for feeding forward anoutput of said sampling means for producing at least one other past timevalue of the sampled data signal, means for combining both past timevalues with the sampled data signal for producing a signal area definedfor an interval and above the amplitude of one of said past time valuesignals thereby providing the estimated rate of change value.
 10. Thegas measurement and analysis system of claim 9 in which said samplingmeans includes means for converting said time varying signal to digitalform thereby to provide said sampled data signal in digital form. 11.The gas measurement and analysis system of claim 10 in which saidsampling means includes means for sampling said time varying signal atequally spaced time intervals to provide said sampled data signal in theform of a series of equally spaced amplitude dependent digital signals.12. The gas measurement and analysis system of claims 10, 11 or 9 inwhich said feeding forward means includes means for delaying the sampleddata signal from said sampling means by a predetermined number of sampletimes thereby to produce a delayed sampled data value.
 13. The gasmeasurement and analysis system of claim 12 in which said feedingforward means includes means for further delaying said delayed sampleddata value and means for producing the difference between said delayedsampled data value and said further delayed sampled data value and formultiplying the resultant value by said predetermined number of sampletimes to produce a multiplied difference value.
 14. The gas measurementand analysis system of claim 13 in which said recursive feedback meansincludes further means for delaying the rate of change estimate value toprovide a delayed rate of change estimate value delayed by one timeinterval, and further means for combining said delayed rate of changeestimate value and said multiplied difference value for producing arecursive past time value.
 15. The gas measurement and analysis systemof claim 14 in which said combining means includes means for combiningsaid recursive past time value and said delayed sampled data value withthe sampled data signal for producing said estimated rate of changevalue.